Lecture Notes on Mathematical ModelingThese lecture notes, and especially the exercises, follow the...
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Lecture Notes on Mathematical Modeling Eleftherios Gkioulekas
Transcript of Lecture Notes on Mathematical ModelingThese lecture notes, and especially the exercises, follow the...
Lecture Notes on Mathematical Modeling
Eleftherios Gkioulekas
Copyright c©2010 Eleftherios Gkioulekas. All rights reserved.Permission is granted to make and distribute verbatim copies of this document, only on astrictly non-commercial basis, provided the copyright notice this permission notice, and theavailability information below are preserved on all copies.
These notes are constantly updated by the author. If you have not obtained this file fromthe author’s website, it may be out of date. This notice includes the date of latest update tothis file. If you are using these notes for a course, I would be very pleased to hear from you, inorder to document for my University the impact of this work.
The main online lecture notes website is: https://faculty.utrgv.edu/eleftherios.gkioulekas/You may contact the author at: [email protected] updated: January 11, 2020
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Contents
1 MM1: Introduction 22 MM2: 1D autonomous systems 193 MM3: Linear autonomous systems 584 MM4: Nonlinear autonomous systems 805 MM5: Limit cycles 1226 MM6: Center manifold reduction 168
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MM1: Introduction
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MM2: 1D autonomous systems
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MM3: Linear autonomous systems
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MM4: Nonlinear autonomous systems
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MM5: Limit cycles
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MM6: Center manifold reduction
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References
These lecture notes, and especially the exercises, follow the textbook by Strogatz, but from amore mathematically rigorous standpoint. Below is the list of references were consulted duringthe preparation of these lecture notes.
(1) S.H. Strogatz (1994): ”Nonlinear dynamics and chaos”, Addison-Wesley(2) B. Deconinck (2009): ”Dynamical systems”, online lecture notes(3) S. Wiggins (2003): ”Introduction to Applied Nonlinear Dynamical Systems and Chaos”,
2nd edition, Springer-Verlag
